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The average rainfall in a city for the first four days was recorded to be 0.40 inch. The rainfall on the last two days was in the ratio of4 :3. The average of six days was 0.50 inch. What was the rainfall on the fifth day?
  • a)
    0.60 inch
  • b)
    0.70 inch
  • c)
    0.80 inch
  • d)
    0.90 inch
Correct answer is option 'C'. Can you explain this answer?
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The average rainfall in a city for the first four days was recorded to...
Given:
Average rainfall for the first four days = 0.40 inch
Ratio of rainfall on last two days = 4:3
Average rainfall for six days = 0.50 inch

To find:
Rainfall on the fifth day

Solution:
1. Total rainfall for the first four days = 0.40 x 4 = 1.60 inch
2. Let the rainfall on the fifth day be x inch
3. Total rainfall for six days = 0.50 x 6 = 3.00 inch
4. Total rainfall for the last two days = 4y + 3y = 7y (where y is a common factor)
5. Total rainfall for all six days = 1.60 + x + 7y = 3.00
6. Simplifying, we get: x + 7y = 1.40
7. Since the ratio of rainfall on last two days is 4:3, let the rainfall be 4z and 3z, respectively
8. So, 7y = 4z + 3z = 7z
9. Substituting 7y = 7z in equation (6), we get: x = 1.40 - 7z
10. Since the average rainfall for six days is 0.50 inch, we can write:
(1.60 + x + 7y)/6 = 0.50
(1.60 + 1.40 - 7z + 7z)/6 = 0.50
3/6 = 0.50
1.00 = 0.50
This is not possible, which means our assumption that the rainfall on the fifth day is x inch is wrong
11. Let's assume that the rainfall on the sixth day is y inch
12. So, the total rainfall for all six days can be written as:
1.60 + x + 4z + 3z + y = 3.00
1.60 + x + 7z + y = 3.00
Substituting x = 1.40 - 7z, we get:
1.60 + 1.40 - 7z + 7z + y = 3.00
y = 0.80 inch

Therefore, the rainfall on the fifth day was 0.80 inch (Option C)
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The average rainfall in a city for the first four days was recorded to be 0.40 inch. The rainfall on the last two days was in the ratio of4 :3. The average of six days was 0.50 inch. What was the rainfall on the fifth day?a)0.60 inchb)0.70 inchc)0.80 inchd)0.90 inchCorrect answer is option 'C'. Can you explain this answer?
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